MinT - Best Known (80−55, 80, s)-Nets in Base 32

Best Known (80−55, 80, s)-Nets in Base 32

(80−55, 80, 120)-Net over F₃₂ — Constructive and digital

Digital (25, 80, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 80, 120)-net over F₃₂, using
- net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]

(80−55, 80, 177)-Net in Base 32 — Constructive

(25, 80, 177)-net in base 32, using

28 times m-reduction [i] based on (25, 108, 177)-net in base 32, using
- base change [i] based on digital (7, 90, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(80−55, 80, 225)-Net over F₃₂ — Digital

Digital (25, 80, 225)-net over F₃₂, using

t-expansion [i] based on digital (24, 80, 225)-net over F₃₂, using
- net from sequence [i] based on digital (24, 224)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 24 and N(F) ≥ 225, using
    - a curve from the manYPoints database [i]

(80−55, 80, 8919)-Net in Base 32 — Upper bound on s

There is no (25, 80, 8920)-net in base 32, because

1 times m-reduction [i] would yield (25, 79, 8920)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 80881 279544 542643 950171 150862 543281 529170 372482 655475 240560 035604 071957 537766 157929 841115 429924 263552 868535 463901 281288 > 32⁷⁹ [i]